TECHNICAL BULLETIN - Piping Technology

TECHNICAL BULLETIN

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Copyright © 2009 Piping Technology & Products, Inc.

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Vol. 1 No. 1

SERVICES

TEMPERATURE & STRESS ANALYSIS

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OBJECTIVETo show the results of temperature and stress analysis in three pipe support shoes intended for cryogenic operation

It is necessary to know the temperature distribution for cryogenic conditions because most steels lose ductility as the temperature decreases from normal operating conditions. Th at is, the steel becomes more brittle.

Any steel structure will have local areas of high stress. Th is may be caused by, for example, sharp corners in the design, or by inclusions in the material. At normal temperatures the material in the region of these concentrations will yield, redistributing the load locally. Typically these have no signifi cant eff ect on the integrity of the structure as a whole. In brittle materials, the material cannot yield, so the only alternative is for it to form a crack. Frequently, once the crack has been formed, it will propagate at the approximate speed of sound until it reaches the end of the part, thus causing a catastrophic failure.

Further complicating the picture is the fact that the tendency for brittle fracture increases with part thickness, and this increase is temperature dependent. Clearly, temperature is a critical vari-able in selecting steels for cryogenic applications.

Th e three shoes considered are of the same basic design, but are for three diff erent pipe sizes: 6, 20, and 42 inch. Th e basic design is shown in Figure 1.

[Figure 1: Complete pipe shoe assembly]


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OBJECTIVETh e shoes have three major components. Th ey are: 1. An outer cover and base of carbon steel, shown in Figure 2A. Th is has ring stops at either end to engage the insulation to keep it from moving. A point of particular concern was the temperature and stress of the steel on the inner surface of this ring.

2. A pipe which carries the cryogenic fl uid. Th is has an attached ring of stainless steel, again for engaging the insulation. Th is is shown in Figure 2B.

3. Th e polyurethane foam insulation (PUF) between the fi rst two parts, shown in Figure 2C. As illustrated, the insulation has outer grooves for the shell ring stops, and an inner groove for the pipe ring.

STRESS & THERMAL ANALYSISTh e stress and the thermal analyses are, for the most part, quite similar. Th e fi nite element program, Ansys was used for both. Th ere are two main diff erences between the analyses. Primarily, the material properties are diff erent. Young’s modulus vs. thermal conductivity, for example; the other main diff erence is in the choice of elements. In this case we used Ansys element 92 for the stress analysis, and thermal element 83. Th ese are both 10 node tetrahedral solid elements. Th e primary diff erence is that the thermal element has only one degree of freedom at each node (for temperature), while the stress element has three, one for x, y, and z displacements.

[Figure 2A: Shell] [Figure 2B: Pipe and Ring] [Figure 2C: Insulation]

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STRESS ANALYSISThe main concern in the 42 inch pipe shoe case was the inner surface of the outer retaining rings. If the temperature is too low for the stress, the specifi ed steel may not be appropriate according to the code.

The other two cases are very similar to this one and those stress results are given in Appendix A.

Applied loads for all three cases are given in Table1. Note that while the loads were specifi ed in kN, the actual computations were done in inches and pounds, and the results are reported in those units.

Pipe Size Axial Load Vertical Load Lateral Load42 in 600 kN 175 kN 70 kN20 in 275 kN 65 kN 50 kN6 in 43 kN 25 kN 10 kN

[Table 1: Applied loads for the stress analysis of the three shoes]

[Figure 3: Stresses in the complete assembly for the 42" pipe shoe]

* It is more informative to view the stresses on the individual components.



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STRESS ANALYSISFigure 4 shows an overview of the stresses on the shell and base, and Figure 5 shows a detail of the stresses in the area of maximum stress. The stresses in the shell are generally quite low. However, at the intersection of the base with the cylindrical shell there is a local stress concentration with some-what higher stresses. This should not be a problem at this location. As we shall see, the temperature here is quite high, as compared to the rest of the shoe.

[Figure 4: Stresses in shell and base] [Figure 5: Detail of stresses in thelocation of maximum stress]

The stresses in the pipe and its ring are shown in Figure 6. The stresses are largest where they would be expected, at the intersection of the two.

[Figure 6: Stresses in the pipe and its ring]

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STRESS ANALYSISIn Figures 7 and 8 we show the stresses in the insulation. Figure 7 is an overview. Figure 8 is a cut away view showing stresses on the inside. The fact that the stress is mostly in the bottom quarter is the result of the signifi cant vertical load.

[Figure 7: Stresses in the insulation] [Figure 8: Section detail of insulation stresses]

THERMAL RESULTSFor all three shoes, the thermal conditions were the same. The inner surface of the pipe was -270°F. The ambient air temperature was -20°F, with a wind velocity of 78.74 in/sec (2 m/sec). Based on this wind speed, and the diameter of the outside shield, we computed a fi lm heat transfer coeffi cient. The values for the three cases are shown in Table 2.

[Table 2: File heat transfer coeffi cients used in the study]Pipe Size Coeffi cent

42 in 0.008281 BTU/ in2 hr20 in 0.009651 BTU/ in2 hr6 in 0.01190 BTU/ in2 hr

The values of thermal conductivities used are in Table 3. Note that for the 32 lb PUF case the coeffi cient is linear with temperature. For the 20 Lb PUF we had only one data point, so we were unable to use a temperature dependent relation.

[Table 3: Thermal conductivities for materials used in the study]Material Conductivities in BTU /hr in oF

Carbon Steel 2.645Stainless Steel 0.7846

32 Lb PUF .0.003007-0.000003627*T20 Lb PUF 0.001685



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TEMPERATURE DISTRIBUTIONIn Figure 9 we show the temperature for the complete assembly. As expected, the temperature on the pipe is the specifi ed temperature, and the temperature on the base is slightly lower than the ambient.

[Figure 9: Complete assembly (°F)]

Again, it is helpful to look at the individual parts. Figure 10 shows the temperature on the shell and base. The coldest temperature is greater than -40°F, and thus much higher than the temperature that would cause concern.

[Figure 10: Shell-base assembly (°F)]

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TEMPERATURE DISTRIBUTIONIn Figures 11 and 12 we show the temperature distributions on the other two parts. There is nothing particular to note concerning these plots. (Temperatures are °F)

[Figure 11: Ring and Pipe] [Figure 12: Insulation]

Figure 13 shows the interface between the steel and the insulation. As expected, the tempera-ture in both the inner and outer rings is little aff ected by the temperature in the surrounding insulation, and is nearly the same as if there were no insulation present.

[Figure 13: Section view showing interface between the steel and insulation]

The report includes both the temperature and the stress at each point of the shoe assembly. This should be adequate for a proper selection of steels for the design.



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APPENDIX AIn this Appendix we show the results of the stress analyses of the 20 and 6 in. pipe cases. There is little to add to what has been said about the 42 in. case.

[Figure A1: Stresses in 20 inch assembly]

[Figure A2: Stresses in shell-base part] [Figure A3: Detail of maximum stress]

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APPENDIX A Continued

[Figure A4: Stresses in ringpipe] [Figure A5: Stresses in insulation]

[Figure A6: Cut away view of insulation stresses]

[Figure A7: Overall stresses on 6 inch assembly]



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APPENDIX A Continued

[Figure A8: Shell-Base stresses, 6 inch case] [Figure A9: Detail at maximum stress]

[Figure A10: Stresses in pipe and ring] [Figure A11: S tresses in 6 inch insulation]

[Figure A13: Detail of ring]

[Figure A12: Stresses on insulation section]

At the left, we show a expanded view of the ring - pipe intersection. The high stresses shown in Figure A10 are very local, and only near the pipe end. This is where the loads were applied. The total load is correct, and, as can be seen, stresses near the intersection are more moderate.

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APPENDIX B: Temperature DistributionNote: Temperatures are degrees °F

[Figure B1: Complete assembly for 20 inch pipe shoe]

[Figure B2: Shell-base assembly for 20 inch pipe shoe]

[Figure B3: Pipe-ring assembly for 20 inch pipe shoe]



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[Figure B4: Insulation block for 20 inch pipe shoe]

[Figure B5: Cut away view of insulation block for 20 inch pipe shoe]

[Figure B6: Pipe shoe assembly for 6 inch pipe shoe]

APPENDIX B: Continued

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APPENDIX B: Continued

[Figure B7: shell-base assembly for 6 inch pipe shoe]

[Figure B8: Pipe-ring assembly for 6 inch pipe shoe]

[Figure B9: Insulation for 6 inch pipe shoe]

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